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1997 Turkey Team Selection Test
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Turkey TST 1997 Problem 6, minimum value of sum
Turkey TST 1997 Problem 6, minimum value of sum
Source: Turkey TST 1997 Problem 6
November 30, 2011
inequalities
inequalities proposed
Problem Statement
If
x
1
,
x
2
,
…
,
x
n
x_{1}, x_{2},\ldots ,x_{n}
x
1
,
x
2
,
…
,
x
n
are positive real numbers with
x
1
2
+
x
2
2
+
…
+
x
n
2
=
1
x_{1}^2+x_2^{2}+\ldots +x_{n}^{2}=1
x
1
2
+
x
2
2
+
…
+
x
n
2
=
1
, find the minimum value of
∑
i
=
1
n
x
i
5
x
1
+
x
2
+
…
+
x
n
−
x
i
\sum_{i=1}^{n}\frac{x_{i}^{5}}{x_{1}+x_{2}+\ldots +x_{n}-x_{i}}
∑
i
=
1
n
x
1
+
x
2
+
…
+
x
n
−
x
i
x
i
5
.
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